MIAMI, Fla. — As the race for Florida tightens, Mitt Romney and Newt Gingrich spent Wednesday trying to persuade the Hispanic community that they aren’t hostile to immigrants.

In separate interviews with Univision’s Jorge Ramos, the two Republicans fought over who had the more humane immigration policy and whether Gingrich was pandering when he dubbed Romney “anti-immigrant.”

Though that kind of rhetoric may be red meat to national GOP crowds, it’s not so palatable to Latinos who make up roughly 450,000 of the Republicans who vote in primaries here in Florida, which holds its contest next Tuesday. Polls show the race between Gingrich and Romney tightening, and Latinos — particularly the 1 million Cuban Americans whose community is based in South Florida — will be a key voting bloc for the winner.

Gingrich has some ground to make up, especially after the latest poll of Florida Hispanic voters showed Romney with a 15-point lead over him.

In his interview with Ramos, Gingrich blasted Romney for saying the solution to illegal immigration was “self-deportation,” a line that raised eyebrows when the former Massachusetts governor used it in a debate earlier this week. Gingrich mocked the idea — which means illegal immigrants choosing to leave the country and attempting to return legally — as “an Obama-level fantasy.”

Gingrich’s own immigration policy calls for some illegal immigrants who have been in the country for long periods to be given a path to U.S. citizenship. Gingrich has said that Romney “shows no concern for the humanity of people who are already here.”

“I think you have to live in a world of Swiss Bank accounts and Cayman Island accounts and … you know, $20-million-a-year income with no work to have some fantasy this far from reality,” the former speaker said, referring to Romney’s tax returns released this week.

“Remember that I talked very specifically about people who have been here a long time, who are grandmothers and grandfathers, who have been paying their bills, they have been working, they are part of the community,” Gingrich said. “Now for Romney to believe that somebody’s grandmother is going to be so cut off that she is going to self-deport, I mean, this verges — this is an Obama-level fantasy.”

Speaking to Ramos later, Romney blasted Gingrich’s rhetoric.

“It’s very sad for a candidate to resort to that kind of epithet. It’s just inappropriate,” Romney said, referring to Gingrich’s line that he is “anti-immigrant.” “I’m pro-immigration and pro-immigrant.”

Romney argued that Gingrich had previously also supported self-deportation and was now changing his tone for political purposes.

“I recognize that it’s very tempting coming to an audience like this and to pander to the audience and to say what you hope people will want to hear. But frankly, I think that’s very unbecoming of a presidential candidate, and a mistake on his part.”

But Gingrich also got himself into hot water with GOP Sen. Marco Rubio — to whom he is comparing his insurgent campaign — after airing a Spanish-language ad that suggests Romney is “anti-immigrant.”

“We need to have a practical, honest conversation about how to have a series of steps that get us to legality for the entire country,” Gingrich said.

Demonstrating just how sensitive such language can be in Florida, Gingrich pulled the ad after Rubio — who is remaining neutral in the presidential race — criticized it as “inaccurate and inflammatory.”

“The truth is that neither of these two men is anti-immigrant,” said Rubio, according to The Miami Herald. “Both are pro-legal immigration and both have positive messages that play well in the Hispanic community.”

While both candidates answered questions on a host of issues targeting Florida’s rapidly-growing Hispanic community, Romney stopped short of saying he was one of them.

Asked by Ramos whether he considered himself a Mexican-American — Romney’s father, George, was born in Mexico — Romney laughed off the question.

“I would love to be able to convince people of that, particularly in a Florida primary,” Romney said. Later, he added that people wouldn’t think “I was being honest with them if I said I was Mexican-American.”

On Wednesday, both Romney and Gingrich also delivered policy speeches aimed directly at the Cuban-American community in South Florida.

Gingrich had strong warnings for Fidel Castro, saying he would use all non-military means available to try to remove him from power. While President Barack Obama was encouraging revolution in Arab countries, he was ignoring Cuba, Gingrich claimed.

“I don’t think it’s ever occurred to a single person in the White House to look south and propose a Cuban spring,” Gingrich said. “If [former Egyptian leader Hosni] Mubarak was bad, Castro is worse.”

Mitt Romney also predicted serious consequences for the Cuban leader under his watch.

“If I’m fortunate enough to become the next president of the United States, it is my expectation that Fidel Castro will finally be taken off this planet,” Romney said to cheers from the hundreds gathered to hear his Miami speech.

Castro’s fate is an area of agreement for Romney and Gingrich. But the Cuban leader has lashed out at them and the rest of the Republican primary field.

In a column on a Cuban website, Castro accused the Republican candidates of “idiocy and ignorance” for calling for the overthrow of Cuba’s communist regime.